| In this thesis, the basic knowledge and the achievement of black holes are reviewed, and my work on Hawking radiation, area spectrum and duality of the black holes are introduced. The thesis contains seven chapters, which are listed as follows:The first chapter is the introduction. The formation, evaporation, thermodynamic properties and exploration of black holes are introduced in this chapter.The aim in the second chapter is to extend Parikh and Wilczek's work to the Hawking radiation of massive and charged particles. We adopt the semi-classical tunnelling method to investigate the Hawking radiation of scalar particles in an Einstein-Maxwell-Dilaton-Axion (EMDA) spacetime. The result shows the radiation spectrum is not purely thermal, and the tunnelling rate is related to the change of Bekenstein-Hawking entropy, which is in consistence with the results obtained by Parikh, Wilczek, Zhang and other people. Meanwhile, the complex path integral is applied to the discussion of tunnelling behavior of massive particles in a Taub-Nut spacetime, and the Hawking temperature is derived and in accordance with the former results.The investigation on tunnelling radiation of fermions is presented in the third chapter. The key in this part is to construct gamma matrixes. For axisymmetrical black holes, the mater field in the ergosphere near the horizon is dragged by the gravitational field with an azimuthal angular velocity and the convenience for constructing gamma matrixes; therefore we research the fermions'tunnelling radiation in the dragging field. The result obtained from the research of fermions'tunnelling radiation in de Sitter spacetime shows that a particle with positive frequency has the negative energy measured at the cosmological horizon. The result derived in the investigation of the radiation in Horava-Lifshitz gravity implies that parameters in this gravitation theory restrict the Hawking temperatures.In the fourth chapter, taking Nation's work on the photon's Hawking radiation described by the one-dimensional quantum channel and Bekenstein and Mayo's work of the constraint on black hole's dimensions into account, we regard black holes as one-dimension and adopt the one-dimensional quantum channel to investigate the Hawking radiation of fermions and bosons in Kerr and Kerr-Newman black holes. Meanwhile, the thermal conductance and electric conductance are researched. The result shows black holes'thermal conductance is only related to the gravity and isn't well-proportioned. The electric conductance is only related to the particle's charge. In the investigation, the magnetic quantum number is regarded as general charge, its chemical potential equals the magnetic quantum number multipling the angular velocity.In the fifth chapter, combining Maggiore's new interpretation of QNMs and the first law of thermodynamicsof black holes, we discuss the area spectrum of Schwarzschild de Sitter black hole and Reissner-Nordstrom de Sitter black hole near extremal case. The derived result indicates the area spectrum and entropy spectrums are spaced and unrelated to the black holes'parameters. This result has universality, and can be applied to other non-extremal black holes.The work in the sixth chapter is the extension of Kerr/CFT correspondence. The duality of EMDA black holes in the extreme case and non-extreme case is researched. The result shows there is duality in the“near”regions, but it is spontaneously broken due to the periodicity of the azimuthal angle. For the non-extreme case, the absorption cross section in the“near”region is derived and exactly equals that in a 2D CFT. The microscopic entropy is derived by the Cardy formula and is fully in consistence with the Bekenstein-Hawking area-entropy law. For the extreme case, by redefining the conformal coordinates, the duality between the solution space and CFT is studied. The microscopic entropy is found to exactly agree with the area-entropy law.The seventh chapter contains conclusions and some conceiving of further research. |
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